Hard working Homestead Kitty

So my very loving cat brings me "gifts" all the time leaving them on the steps. She will bring me one every other day or so. My issue is despising of them I bag them up and put the in a covered trash can. By the time trash day rolls around it smells of death and well the other things that come along with rotting stuff. Anyone have a better method of getting rid of the dead presents my cat brings???